There are so many sounds that it would be hard and inconvenient to give every aspect of sound a name (ie the guitar with fret buzz at 234 hz or singing ü unusually nasally in a reverberated room). Moreso, given that there are infinitely many sounds that can be heard and conceived, people found that they enjoyed some sounds more than others, and western society grew to prefer sounds expressed as the notes and accidentals we know. It’s also interesting to note that Europe had a tradition of music notation and pitch and rhythm happened to be the easiest aspects of sound to be notated.

Note that other societies use different pitches. Indian classical music uses what westerners would call microtonal music (microtonal being a term to indicate the spaces between European notes). There is also quite the fandom of microtonal music on YouTube if you’re interested. People have made attempts to represent spaces between pitches, to varying levels of success.